Finite Group DatabasebetaFinite Group Databasebeta| order | 37620 |
| automorphism | ? |
| homology | Abelianization (H1) = C11 · Schur multiplier (H2) = C2 |
| direct product | C11×PSL(2,𝔽19) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C11 | PSL(2,𝔽19) |
| commutator, hypocenter | PSL(2,𝔽19) | C11 |
| Frattini | C1 | G |
| LCS | G ▷ PSL(2,𝔽19) | |
| UCS | C1 ◁ C11 | |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 220 |
A minimal faithful permutation representation — 2 generators on 31 points:
(12,25,15,30,22,13,17,14,28)(16,31,26,19,29,23,20,18,27);(1,2,3,4,5,6,7,8,9,10,11)(12,31,13,28,15,27,14,22,24,19,26,29,25,17,23,18,20,21,30)132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37620, 507);